Preheat your grill to direct, medium-high heat.

Using kitchen shears, remove an inch from the top of the artichokes. Also remove the sharp points from the tips of the leaves. Artichokes can be very difficult to cut even with your sharpest knife. Kitchen shears work much better.

Use a paring knife to remove the small leaves near the bottom of the artichoke and cut off the bottom of the stem, leaving about an inch. Then use a vegetable peeler to remove the tough outer skin of the artichoke stem.

Boiling the artichokes ensures the tender hearts cook evenly before grilling. Fill a large pot with enough water to cover the artichokes with about an inch of water. Add the kosher salt and bring the water to a boil. Place the artichokes in the boiling water, stem side down. The artichokes will float, and that’s OK. Cover the pot with a lid and boil for 18-20 minutes.

While the artichokes are cooking, prepare the aioli. In a small bowl, whisk together the mayonnaise, lemon juice, garlic, kosher salt and black pepper.

Remove the artichokes from the water and turn them upside down to drain. Pat them dry with paper towels. Let them rest for about 15 minutes.

Using a sharp knife, slice the artichokes in half and remove any loose leaves. Scoop out the fuzzy choke at the center using a small spoon or tip of a serrated knife, like a grapefruit knife.

Place the artichoke halves cut-side down on the hot grill. Cook the artichoke halves on the grill until they develop grill marks and turn golden brown, about 5 minutes. Flip them over and grill the other side for 3-4 minutes. Serve with the aioli and lemon wedges.